Proper asymptotic unitary equivalence in \KK-theory and projection lifting from the corona algebra

2010/09/14 by Lee, Hyun Ho · 1 citation
#46L35 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1009.2592

Abstract

In this paper we generalize the notion of essential codimension of Brown, Douglas, and Fillmore using \KK-theory and prove a result which asserts that there is a unitary of the form `identity + compact' which gives the unitary equivalence of two projections if the `essential codimension' of two projections vanishes for certain C\sp*-algebras employing the proper asymptotic unitary equivalence of \KK-theory found by M. Dadarlat and S. Eilers. We also apply our result to study the projections in the corona algebra of C(X)⊗ B where X is [0,1], (-∞, ∞), [0,∞), and [0,1]/\0,1\.

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